Gambler's Ruin - Expository Introduction with diagrams

The Gambler's Ruin problem explained as a conditional probability. For any given amount \(h\) of current holdings, the conditional probability of reaching \(N\) dollars before going broke is independent of how we acquired the \(h\) dollars, so there is a unique probability \(Pr{N|h}\) of reaching \(N\) on the condition that we currently hold \(h\) dollars. Boundary conditions are imposed. Plots are shown for various probability of winning one round. The case when that probability equals 1/2 is explained. A nice graphic for the Markov model is shown.